Wed, 2010-09-29 17:57 — ggoncalv@brown.edu

Title | Estimating the tensor of curvature of a surface from a polyhedral approximation |

Publication Type | Conference Paper |

Year of Publication | 1995 |

Authors | Taubin, G. |

Publisher | IEEE Computer Society |

Keywords | computational geometry computer vision eigenvalues eigenvalues and eigenfunctions eigenvectors integral formulas iso-surface construction algorithms matrix representation medical applications polyhedral approximation polyhedral surface principal curvature |

Abstract | Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by iso-surface construction algorithms, has become a basic step in many computer vision algorithms, particularly in those targeted at medical applications. We describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain 3/spl times/3 symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface. |